Hudson was marked wrong on this problem, but why? Explain what error he made and include the correct method for solving this problem.

Answer:

A = 7.5 units^2

Step-by-step explanation:

A = (a+b)/2 * h

A and B are both bases of the trapezoid (top and bottom)

H is the height

A is 1

B is 4

H is 3

Plug that into the trapezoid equation and we get

(1+4)/2 * 3 = 7.5 units ^2

If the factor of the function are (x - 3), (x + 3), and (x + 1). Then the zeroes of the function will be negative 3, 3, and negative 1. Then the correct option is A.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The function is given below.

[tex]\rm f(x) = (x^2 - 9) (x +1)[/tex]

The function can be written as

[tex]\rm f(x) = (x^2 - 3^2) (x +1)\\\\\rm f(x) = (x - 3)(x+ 3) (x +1)[/tex]

If the factor of the function are (x - 3), (x + 3), and (x + 1). Then the zeroes of the function will be negative 3, 3, and negative 1.

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From the graph, we concluded that line passes through the points (0, 3) and (1, 4) respectively.

So, slope of the line (m) passing through the points (a, b) and (c, d) is

m = d - b/ c - a

m = 4 - 3 / 1 - 0 = 1/1 = 1

Also, line makes an intercept of 3 units in positive direction of y - axis.

So, c = 3

y = mx + c

y = 1 × x + 3

We know, Equation of line passing through the points (a,b) and (c, d) is given by

y - b = d - b / c - a (x - a)

a = 0

b = 3

c = 1

d = 4

y - 3 = 4 - 3 /1 - 0 ( x - 0 )

y - 3 = 1/1 ( x - 0 )

y - 3 = x

1. Equations of horizontal and vertical lines

Equation of line parallel to x - axis passes through the point (a, b) is y = b.

Equation of line parallel to y - axis passes through the point (a, b) is x = a.

Equation of line passing through the point (a, b) having slope m isy - b = m(x - a)

Equation of line which makes an intercept of c units on y axis and having slope m is y = mx + c.

Equation of line which makes an intercept of a and b units on x - axis and y axis respectively is x/a + y/b = 1.

Equation of line which is at a distance of p units from the origin and perpendicular makes an angle B with the positive X-axis is x cosB + y sinB = p.

Answer:

it's a bit hard to see in green.

Answer:

L=8cm W=5cm

Step-by-step explanation:

8+8=16

5+5=10

10+16=26cm

5x8=40cm

The correct option is:

"A closed circle at (2 + 8/9) and the arrow points to the left"

Here we have the inequality:

(2 + 8/9) ≥ x

First, because the symbol ≥ is used, we need to put a closed circle at (2 + 8/9) which means that the value is an actual solution (open circles are used for < and >), and then we shade all the numbers to the left of that value (because x also could be smaller than that).

Then the correct option is:

"A closed circle at (2 + 8/9) and the arrow points to the left"

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Answer: a closed circle on 2 8/9 and the arrow points to the left

Step-by-step explanation:

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Answer:

x ≥ 18

Step-by-step explanation:

2(x-3)-3(5x-2) ≤ 6(3-2x)

⇔ 2x - 6 - 15x + 6 ≤ 18 - 12x

⇔ 2x - 15x  ≤ 18 - 12x

⇔ -13x ≤ 18 - 12x

⇔ -13x + 12x ≤ 18

⇔ -x ≤ 18

⇔ x ≥ 18

⇔ x∈[18 , ∞)

Answer:If bees disappeared completely, the biodiversity of our planet would be greatly affected, depriving us of various plant species we eat and leading to the disappearance of thousands of species of plants, flowers and fruit trees, as well as honey.

Step-by-step explanation:

Answer:

 D is your answer  Outlier An extreme value in a set of data which is much higher or lower than the other numbers.

Step-by-step explanation:

Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data

Answer:

88.0 in^3 to nearest tenth.

Step-by-step explanation:

The radius = 1/2 diameter

= 11/2 * 4 = 2 ins,

The Volume = πr^2 h

= π * 2^2 * 7

= 87.96 in^3.

Answer:

87.9 in³ OR 88.0 in³

Step-by-step explanation:

Concepts

The volume of a cylinder is [tex]\pi r^2h[/tex], where r = radius and h = height.

The radius is twice the diameter.

Application

We are given the diameter as 4 inches, so the radius is 2 inches. The height of the cylinder is 7 inches. Now, we just apply our aforementioned formula and plug in its values of r and h. Since I don't know if you're using pi as 3.14 or just using the exact value of pi, I have provided two different answers at the top.

Solution

1:

2:

Answer:

The correct answer is B.

Step-by-step explanation:

There seems to be no strong correlation for scatter plot B.

Hope this helps:) Goodluck!

The lateral surface area is about 105,600 meters.

The area of ​​the pyramid is the measure relative to its surface and is obtained by the sum of the areas of the bases (polygonals) and of all the lateral faces (triangles). For the calculation of the lateral area of ​​a pyramid, we will have the perimeter of the base by the inclined height of the pyramid.

In this case, the formula of the lateral surface area is:

[tex]SA=\frac{P*S}{2}+B[/tex]

Where:

The height informed will not be used, it will only be a parameter to perform pythagoras, that is, we will find the hypotenuse of the triangle created by the height, like this:

[tex]S=\sqrt{(B)^2/2+H^2} \\S=\sqrt{110^2+70^2}\\S=\sqrt{17,000}\\ S=130[/tex]

Returning to the formula given above, we find that:

[tex]SA= \frac{(220*4)(130)}{2}+(220*220)\\ SA= 57,200+48,400= 105,600 \ meters[/tex]

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Answer:

yes.The medium plant cannot be the same price of a large price cause of the size difference

Hence the medium plant being nearly half the price of the large plant

Answer:

The quadratic equation [tex]2\, x^{2} - 3\, x + 8 = 0[/tex] has no real solution.

Step-by-step explanation:

Rewrite the quadratic equation [tex]2\, x^{2} - 3\, x + 8 = 0[/tex] in the standard form [tex]a\, x^{2} + b\, x + c = 0[/tex]:

[tex]2\, x^{2} + (-3)\, x + 8 = 0[/tex], for which:

The quadratic discriminant of [tex]a\, x^{2} + b\, x + c = 0[/tex] is [tex](b^{2} - 4\, a\, c)[/tex].  The quadratic discriminant of [tex]2\, x^{2} + (-3)\, x + 8 = 0[/tex] would be:

[tex]\begin{aligned}& b^{2} - 4\, a\, c \\ =\; & (-3)^{2} - 4 \times 2 \times 8 \\ =\; & (-55)\end{aligned}[/tex].

Since the quadratic discriminant of this equation is negative, this quadratic equation has no real solution.

Answer:

Below.

Step-by-step explanation:

You have a data point 5 to the left.

So you would move another data point 5 units to the right - like for example 14 to 19.

Answer:

  10 units

Step-by-step explanation:

Compare the given equation to the standard-form equation for a circle to identify the relevant dimension.

The equation of a circle is written in standard form as ...

  (x -h)² +(y -k)² = r² . . . . . . . centered at (h, k) with radius r

__

Comparing this to what you are given, you see that ...

  h = -25/4

  k = 0

  r² = 25

The radius is ...

  r = √25 = 5

The diameter is twice the radius, so is ...

  d = 2r = 2(5)

  d = 10

The diameter of the circle is 10 units.

Answer:

-0.72

Step-by-step explanation:

First we must solve what in parenthesis

Now we must convert [tex]\frac{9}{14}[/tex] to a whole number

To do that simply divide 9 by 14 and that come out as

= 0.6

Now multiply

Answer:

1 Truncation

Truncation is a method of approximating numbers. It is easier than rounding, but does not always give the best approximation to the original number. Truncation is used in computing when division is done with integers and the answer must be an integer.

Step-by-step explanation:

p (a vanilla cookie) = 6/19

p (a chocolate or lemon cookie) = 13/19

p (not a lemon cookie) = 10/19

p (a vanilla or chocolate or lemon) = 10/19

p (a peanut butter cookie) = [There's no peanut in the info you gave, sorry]

If you can simplify the fractions, then simplify

Answer:

See picture above

Explanation:

Hope this helps and have a nice day

Answer:

let X be the number of ways they can be seated without condition,

let M the the number of ways they can be seated if the two people must sit together,

let N be the number of ways they can be seated if the two must not sit together.

X=7! =5040

M= 6!× 2!=1440

M+N=X

then N=X–M=5040–1440=3600ways

George spend 5 hours driving on the Interstate if George spent two more hours on the Interstate than on the highway.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the George spend x hours on the interstate and (x+2) hours on the highway.

570 = 75x + 65(x-2)

570 = 75x + 65x -130

700 = 140x

x = 5 hours

Thus, George spend 5 hours driving on the Interstate if George spent two more hours on the Interstate than on the highway.

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Step-by-step explanation:

the original retail price was 120% of the manufacturer price (100% manufacturer price + 20% markup).

now, the whole retail price is reduced by 12%.

that means we have to subtract 12% from the 120%.

but careful, we cannot just do 120-12=108.

that is simply because these 120% are now for this calculation the new basic amount and therefore 100%.

we actually need to calculate and subtract 12% of 120 to get the new percentage over the manufacturer price.

we do this by multiplying 120 by (100-12)/100 = 88/100 = 0.88 :

120 × 0.88 = 105.6%

so, the new retail price is now only 5.6% over the manufacturer price.

Answer:

y = 1/3x + 1

Step-by-step explanation:

Answer:[tex]y = \frac{1}{3}x +1[/tex]

Step-by-step explanation:

I can see that one coordinate is (0,1) and another to assume is (-3,0)

With this we can make the equation

Equation format is y = mx + b

b is y-intercept, so when x is 0, y = 1, so b = 1

y = mx + 1

We can substitute (-3,0) into the equation and get 0 = -3m + 1

Solving for m gives us [tex]\frac{-1}{-3} = m[/tex]

so [tex]y = \frac{1}{3}x +1[/tex]

Considering the definition of probability,  the probability that the first movie selected is an comedy movie and the second movie is a action film is 30%.

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

[tex]P(A)=\frac{number of favorable cases}{number of possible cases}[/tex]

The multiplication rule or product rule allows you to find the probability that event A and event B occur at the same time.

Two events A and B are dependent if the occurrence of one affects the occurrence of the other. For dependent events, the multiplication rule states that:

P(A∩B)= P(A)× P(B|A) (where P(B|A) indicates “the probability of ‘B’ having occurred ‘A’)

In this case, you know:

The probability that the first movie selected is an comedy movie and the second movie is a action film.

Once the first movie is selected, there are no longer 6 movies available. There are only 5, because one of the options is eliminated. So the occurrence of the first event affects the second event and the events are dependent.

Then, the probabilty can be calculated A:

Probability= [tex]\frac{3}{6}[/tex]× [tex]\frac{3}{5}[/tex]

Probability= 0.3= 30%

Finally, the probability that the first movie selected is an comedy movie and the second movie is a action film is 30%.

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Given that, Darlene can finish an average-sized crocheted centerpiece for 2 week, the number of days it will take her to finish 4 projects is  56 days.

Given that;

If 1 project takes 14 days

4 project takes x days

x = 4 × 14 days

x  = 56 days

Given that, Darlene can finish an average-sized crocheted centerpiece for 2 week, the number of days it will take her to finish 4 projects is  56 days.

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Answer:

(x-3)*(4x+1)

Step-by-step explanation:

Factoring  4x2-11x-3

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -11x  its coefficient is  -11 .

The last term, "the constant", is  -3

Step-1 : Multiply the coefficient of the first term by the constant   4 • -3 = -12

Step-2 : Find two factors of  -12  whose sum equals the coefficient of the middle term, which is   -11 .

     -12    +    1    =    -11    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  1

                    4x2 - 12x + 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

                   4x • (x-3)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-3)

Step-5 : Add up the four terms of step 4 :

                   (4x+1)  •  (x-3)

            Which is the desired factorization

Final result :

 (x - 3) • (4x + 1)

Answer:

[tex](4x+1)(x-3)[/tex]

Step-by-step explanation:

[tex](4x+1)(x-3)=4x^{2} +x-12x-3=4x^{2} -11x-3[/tex]

Hope this helps

Answer :

[tex]x < 2[/tex]